Multivariate modelling of variability in sheet metal forming

The inherent variability in incoming material and process conditions in sheet metal forming makes quality control and the maintenance of consistency extremely difficult. A single FEM simulation is successful at predicting the formability for a given system, however lacks the ability to capture the variability in an actual production process due to the numerical deterministic nature. This paper investigates a probabilistic analytical model where the variation of five input parameters and their relationship to the sensitivity of springback in a stamping process is examined. A range of sheet tensions are investigated, simulating different operating windows in an attempt to highlight robust regions where the distribution of springback is small. A series of FEM simulations were also performed, to compare with the findings from the analytical model using AutoForm Sigma v4.04 and to validate the analytical model assumptions.Results show that an increase in sheet tension not only decreases springback, but more importantly reduces the sensitivity of the process to variation. A relative sensitivity analysis has been performed where the most influential parameters and the changes in sensitivity at various sheet tensions have been investigated. Variation in the material parameters, yield stress and n-value were the most influential causes of springback variation, when compared to process input parameters such as friction, which had a small effect. The probabilistic model presented allows manufacturers to develop a more comprehensive assessment of the success of their forming processes by capturing the effects of inherent variation.